Problem: Simplify the following expression: $ r = \dfrac{5}{8} + \dfrac{3}{-10k - 9} $
Explanation: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{-10k - 9}{-10k - 9}$ $ \dfrac{5}{8} \times \dfrac{-10k - 9}{-10k - 9} = \dfrac{-50k - 45}{-80k - 72} $ Multiply the second expression by $\dfrac{8}{8}$ $ \dfrac{3}{-10k - 9} \times \dfrac{8}{8} = \dfrac{24}{-80k - 72} $ Therefore $ r = \dfrac{-50k - 45}{-80k - 72} + \dfrac{24}{-80k - 72} $ Now the expressions have the same denominator we can simply add the numerators: $r = \dfrac{-50k - 45 + 24}{-80k - 72} $ $r = \dfrac{-50k - 21}{-80k - 72}$ Simplify the expression by dividing the numerator and denominator by -1: $r = \dfrac{50k + 21}{80k + 72}$